Trimming complexes and applications to resolutions of determinantal facet ideals

Authors

• Keller VandeBogert, University of KentuckyFollow

Abstract

We produce a family of complexes called trimming complexes and explore its applications. We demonstrate how trimming complexes can be used to deduce the Betti table for the minimal free resolution of the ideal generated by certain subsets of a generating set for an arbitrary ideal I. In particular, we compute the Betti table of the ideal obtained by removing an arbitrary generator from the ideal of submaximal pfaffians of a generic skew symmetric matrix M. We also explicitly compute the Betti table for the ideal generated by certain subsets of the generating set of the ideal of maximal minors of a generic n × m matrix. Such ideals are a subset of a class of ideals called determinantal facet ideals, whose higher degree Betti numbers had not previously been computed.

Document Type

Article

Publication Date

1-1-2020

Notes/Citation Information

Publisher Copyright: © 2020 Taylor & Francis Group, LLC.

Digital Object Identifier (DOI)

10.1080/00927872.2020.1826043

Archival?

Archival

Repository Citation

VandeBogert, Keller, "Trimming complexes and applications to resolutions of determinantal facet ideals" (2020). Mathematics Faculty Publications. 80.
https://uknowledge.uky.edu/math_facpub/80